Curie's Law & the Three Families
Heat weakens magnetism; ferromagnets switch off above T_c.
Lesson at a glanceShow the key points
- Paramagnets: χ = c/T (37.9).
- Ferromagnets become paramagnetic above T_c: χ = c/(T − T_c) (37.10); iron 1043 K, nickel 631 K.
- Dia: weakly repelled, rod across B; para: weakly attracted, rod along B; ferro: strongly attracted, hysteresis, permanent magnets.
Heat fights magnetism. For paramagnets this follows a simple law; ferromagnets lose their special powers altogether above a definite temperature.
Curie’s law
Raising the temperature randomizes atomic moments more, so at a given H the magnetization, and hence χ, falls. Far from saturation, a paramagnet obeys:
A ferromagnet heated past its Curie temperature Tc becomes paramagnetic, after which
| Ferromagnetic substance | Curie temperature T_c (K) |
|---|---|
| Iron | 1043 |
| Cobalt | 1394 |
| Nickel | 631 |
| Gadolinium | 317 |
| Fe₂O₃ | 893 |
A toroid with a circumference of 30 cm has 600 turns carrying 1.5 A, wound on an aluminium ring at 290 K. The magnetization of the ring is 6.6 × 10⁻² A/m. (a) Find χ. (b) What is the magnetization if the ring is warmed to 350 K?
Comparing the three families
| Diamagnetic | Paramagnetic | Ferromagnetic | |
|---|---|---|---|
| Magnetization in a field | small, opposite to the field | small, along the field | large, along the field |
| χ | small, negative | small, positive (≈ 10⁻⁵ to 10⁻³) | large, positive (thousands) |
| μ_r | slightly below 1 | slightly above 1 | thousands |
| Field lines inside | spread out | slightly crowded | strongly crowded |
| Near a magnet | weakly repelled | weakly attracted | strongly attracted |
| χ vs temperature | almost constant | ∝ 1/T | complicated; paramagnetic above T_c |
| States of matter | solid, liquid, gas | solid, liquid, gas | normally solid only |
| Permanent magnets, hysteresis | no | no | yes |
A rod hung freely between the poles of a magnet settles along the field if it is paramagnetic or ferromagnetic, and across the field if it is diamagnetic.
- 1Curie's law for paramagnets: χ = c/T (37.9).
- 2Ferromagnets become paramagnetic above T_c: χ = c/(T − T_c) (37.10); iron 1043 K.
- 3Dia: χ < 0, repelled, rod across the field; para: χ > 0 small, attracted, rod along it; ferro: huge χ, strongly attracted, hysteresis.
Check yourself
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